Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions

DOI10.1007/S00009-013-0338-1zbMath1294.34029OpenAlexW1965235672MaRDI QIDQ2454110

Aliasghar Jodayree Akbarfam, Isa Dehghani

Publication date: 12 June 2014

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-013-0338-1

zbMATH Keywords

Sturm-Liouville problemsresolvent operatorGreen functiontransmission conditionseigenparameter-dependent boundary conditionsself-adjoint

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General theory of ordinary differential operators (47E05) Green's functions for ordinary differential equations (34B27) Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter (34B07)

Related Items (9)

The Parseval identity for \(q\)-Sturm-Liouville problems with transmission conditions ⋮ Green function and resolvent operator of a Schrödinger equation with general point interaction ⋮ Generalized Fourier series as Green's function expansion for multi-interval Sturm-Liouville systems ⋮ Weyl function of Sturm-Liouville problems with transmission conditions at finite interior points ⋮ On a spectral theory of singular Hahn difference equation of a Sturm‐Liouville type problem with transmission conditions ⋮ Spectral expansion for the singular Dirac system with impulsive conditions ⋮ Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter: Hilbert space formulation ⋮ Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter: eigenvalue asymptotics ⋮ Titchmarsh-Weyl theory for Dirac systems with transmission conditions

Cites Work

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• On inverse Sturm-Liouville problems with spectral parameter linearly contained in the boundary conditions
• Discontinuous Sturm-Liouville problems with eigenparameter-dependent boundary and transmissions conditions
• Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. II
• Sturm-Liouville problems with discontinuities at two points
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Problems for Ordinary Differential Equations with Transmission Conditions

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